Computations and Abbreviations for Bone Histomorphometry - Expanded

In Bone Histomorphometry: Standardization of Nomenclature, Symbols, and Units, Parfitt and colleagues cataloged and standardized the various derivative computations used in bone histomorphometry. An update of the standard nomenclature by Dempster and colleagues was published in late 2012 which introduced additional computations. As the discipline has expanded, additional terms were needed that do not appear in either the original publications or the 2012 update.

In addition to the standard nomenclature, the publications provide canonical computational formulas and definitions for histomorphometric indices. These are provided below the table of abbreviations.

This expanded version is based on the revised table from the 2012 update and is maintained by BIOQUANT to document computations used in our analysis templates. Any non-canonical terms and notes added by BIOQUANT are indicated in bold type.

Standardized Abbreviations Used in BIOQUANT OSTEO

A - L

A
Apposition, Appositional
Ab
Absolute
Ac
Activation
Ad
Adipocytea
Al
Aluminum
Aj
Adjusted
Ar
Area (2D)b
At
Articular
a
Active, Activity
B
Bone
BMU
Basic Multicellular Unit
Bd
Boundary (2D)b
C
Core
Ca
Canal, Canalicula, Canalicular
Cd
Corrected
Ce
Cell
Cg
Cartilage
Ch
Chondrocyte
Cl
Calcificationk
Cm
Cement
Cn
Cancellous
Co
Contact
Cp
Cytoplasm, Cytoplasmic
Cs
Callus
Ct
Cortex, Cortical
Cv
Calvaria, Calvarium, Calvarial
Cy
Cycle
D
Dimension, Dimensional
De
Depth
Df
Differentiating, Differentiation
Dg
Degenerative, Degeneration
Dm
Diameter
Dn
Densityj
Do
Domain
Dp
Diaphysis, Diaphyseal
Dt
Delta
d
Doublec
E
Eroded, Erosion
Ec
Endocortical
Em
Empty
En
Envelope
Ep
Epiphysis, Epiphyseal
Er
Endocranium, Endocranial
Es
Endosteal, Endosteumd
Ex
External
F
Formatione
Fa
Fat, Fatty
Fb
Fibrosis, Fibrous
Fe
Iron
Fr
Front
f
frequency
G
Growth, Growing
H
Haversian
Hm
Hematopoetic
Hp
Hypertrophic
Ht
Height
Hz
Horizontal
h
Hit
I
Interfacef (3D)b
Ia
Intra
Ic
Intercept
If
Inflammatory
Il
Initial
Im
Implant
In
Internal
Ir
Inter
Is
Instantaneous
It
Interstitial
i
Intersection
L
Label, Labeled
Lc
Lacuna, Lacunarg
Le
Length
Li
Lining
Lm
Lamella, Lamellar
Ln
Line
Lo
Longitudinal
l
lag

M - Z

M
Mineral, Mineralizing, Mineralization
Ma
Marrow
Md
Mineralized
Me
Medullary
Mf
Myofiber
Mk
Megakaryocyte
Ml
Modeling
Mn
Mean
Mo
Mononuclear, Mononucleated
Mp
Metaphysis, Metaphyseal
Ms
Muscle
Mt
Myocyte
Mu
Multinuclear, Multinucleated
Mx
Matrix
M
Maturation
N
Number of profiles or structures
N
Number of sampling unitsh
Nc
Nuclear, Nucleus, Nuclei
Nd
Node
Nw
New
O
Osteoid
Ob
Osteoblast, Osteoblastic
Oc
Osteoclast, Osteoclastic
On
Osteon, Osteonal
Os
Ossificationk
Ot
Osteocyte, Osteocytic
P
Period
Pc+
PCNA+
Pf
Profile
Pg
Proteoglycan
Pl
Plate
Pm
Perimeter (2D)b
Pn
Pericranium, Pericranial
Po
Pore, Porous, Porosity
Pr
Proliferating, Proliferative
Ps
Periosteal, Periosteum
Pt
Point
Px
Proximal
Q
Quiescent
R
Rate
Rd
Radial, Radius
Rf
Reference, Referent
Rm
Remodeling
Rs
Resorptione
Rv
Reversal
S
Surface (3D)b
Sa
Sample(ing)
Sb
Subchondral
Sc
Scaffold
Se
Section
Sg
Sigma
Sm
Seam
Sn
Spongiosa
Sp
Separation
St
Structure, Structural
s
single
T
Tissue
Tb
Trabecula, Trabeculari
Th
Thickness (3D)b
Tm
Terminal, Terminus
Tn+
TUNEL+
Tr
Transitional
Tt
Total
Tu
Tumor
t
Time
U
Unit
V
Volume (3D)b
Vd
Void
Vk
Volkmann
Vt
Vertical
W
Wall
Wi
Width (2D)b
Wo
Woven
y
Year
Z
Zone

Standard Units and Formulas in Rodent Histomorphometry

STRUCTURAL INDICES

  • TV (Tissue Volume) mm2
    The total area within the region of interest. Primary data are collected in μm2.

  • BV (Bone Volume) mm2
    The total area of bone, both mineralized bone and osteoid within the tissue volume. Primary data are collected in μm2.

  • BV/TV %
    Bone Volume normalized by Tissue Volume.

  • BS (Bone Surface) mm
    The total perimeter of the bone within the Tissue Volume. Does not include the surface segements where the bone crosses out of the Tissue Volume. Primary data are collected in μm.

  • BS/BV mm-1
    Bone Surface normalized by Bone Volume. The ratio of surface area to volume of a structure is known as the surface to volume ratio. Spheres have the lowest surface area to volume ratio. Highly irregular and complex structures generally have a higher surface area to volume ratio. Read more at the Wikipedia.

  • Tb.Dm (Trabecular Diameter) mm
    Tb.Dm = 4*(BV/BS). Rode Model.

  • Tb.N (Trabecular Number) mm-1
    Tb.N = SQRT(4/3.141*BV/TV)*(1/Tb.Dm). Rod Model.

  • Tb.Sp (Trabecular Spacing) mm
    Tb.Sp = (SQRT(3.141/4*TV/BV)-1)*Tb.Dm. Rod model.

OSTEOBLAST INDICES

  • Ob.N/BS #/mm
    Number of Osteoblasts per unit of Bone Surface.

  • Ob.S/BS %
    Osteoblast Surface as a Percentage of Bone Surface.

  • O.Wi μm
    The mean of all osteoid seam widths in the animal. Widths are measured perpendicularly at regular intervals along the surface. Primary data are collected in μm.

OSTEOCLAST INDICES

  • Oc.S (Osteoclast Surface) mm
    The length of bone surface occupied by the osteoclast. Primary data are collected in μm.

  • Oc.N (Osteoclast Number) #
    Number of osteoclasts is equal to the number of osteoclast surface measurements.

  • Oc.N/BS #/mm
    Number of Osteoclasts per millimeter of Bone Surface.

  • Oc.S/BS %
    Osteoclast Surface normalized by Bone Surface.

FORMATION INDICES

  • sLS (Single Labeled Surface) mm
    Bone surfaces with a single fluorescent label present. Primary data are collected in μm.

  • dLS (Double Labeled Surface) mm
    Bone surfaces with two fluorescent labels present. Primary data are collected in μm.

  • MS (Mineralizing Surface) mm
    MS = sLS/2+dLS.
    The logic here is that MS is the amount of surface of the bone that was mineralizing over the entire labeling period. The assumption is that some of the single label was active at the beginning of the period and some at the end. Labeling with once with calcein and once with alizarin red instead of calcein twice could help sort out this question. But, in general, labs just use calcein and say that half the single label was active at the beginning and half as active at the end. Hence, sLS/2 is the amount of single labeled surface that was active for the whole period.

  • Ir.L.Wi (Interlabel Width) μm
    The mean of all direct measurements of distance between labels in double labeled surfaces. Distances are measured perpendicularly at regular intervals along the surface. Primary data are in collected μm.

  • Ir.L.t (Interlabel Time) days
    The time between injections used to label the mineralizing surfaces.

  • MAR (Mineral Apposition Rate) μm/day
    MAR = Ir.L.Wi/Ir.L.t.

  • Aj.AR (Adjusted Apposition Rate) μm/day
    If MS/OS < 1, then Aj.Ar = MAR*MS/OS. If MS/OS > 1, Aj.Ar = MAR.

  • BFR/BS (Bone Formation Rate, Normalized by Bone Surface) μm/day
    BFR/BS = MAR*MS/BS.

  • BFR/BV (Bone Formation Rate, Normalized by Bone Volume) (μm/day)/mm
    BFR/BV = MAR*MS/BV.

  • BFR/TV (Bone Formation Rate, Normalized by Tissue Volume) (μm/day)/mm
    BFR/TV = MAR*MS/TV.

  • Omt (Osteoid Maturation Time) days
    Omt = O.Wi/MAR.

  • Mlt (Mineralization Lag Time) days
    Mlt = O.Wi/Aj.Ar.

Standard Units and Formulas in Human Histomorphometry

STRUCTURAL INDICES

  • TV (Tissue Volume) mm2
    The total area within the region of interest. Primary data are collected in μm2.

  • BV (Bone Volume) mm2
    The total area of bone, both mineralized bone and osteoid within the tissue volume. Primary data are collected in μm2.

  • BV/TV %
    Bone Volume normalized by Tissue Volume.

  • BS (Bone Surface) mm
    The total perimeter of the bone within the Tissue Volume. Does not include the surface segements where the bone crosses out of the Tissue Volume. Primary data are collected in μm.

  • BS/BV mm-1
    BS/BV = (BS/BV)*1.2.
    Bone Surface normalized by Bone Volume. The ratio of surface area to volume of a structure is known as specific surface area. Spheres have the lowest surface area to volume ratio. Highly irregular and complex structures generally have a higher surface area to volume ratio. Read more at the Wikipedia.

    Additionally, there is a known stereology conversation of 1.2 that compensates for changes in surface when it is viewed as a 1 dimensional length cross-section rather than a 2 dimension surface.

  • Tb.Th (Trabecular Thickness) mcm
    Tb.Th = 2/(BV/BS)*1000. Plate Model.

  • Tb.N (Trabecular Number) mm-1
    Tb.N = (BV/TV)/(2/(BS/BV)). Plate Model.

  • Tb.Sp (Trabecular Separation) mcm
    Tb.Sp = (1/Tb.N)*1000-Tb.Th. Plate Model.

OSTEOBLAST INDICES

  • Ob.N/BS #/mm
    Number of Osteoblasts per unit of Bone Surface.

  • Ob.S/BS %
    Osteoblast Surface as a Percentage of Bone Surface.

  • O.Wi μm
    Average(O.Wi)/1.2.
    The mean of all osteoid seam widths in the biopsy corrected by a known stereology constant of 1.2. Widths are measured perpendicularly at regular intervals along the surface. Primary data are collected in μm.

OSTEOCLAST INDICES

  • Oc.S (Osteoclast Surface) mm
    The length of bone surface occupied by the osteoclast. Primary data are collected in μm.

  • Oc.N (Osteoclast Number) #
    Number of osteoclasts is equal to the number of osteoclast surface measurements.

  • Oc.N/BS #/mm
    Number of Osteoclasts per millimeter of Bone Surface.

  • Oc.S/BS %
    Osteoclast Surface normalized by Bone Surface.

FORMATION INDICES

  • sLS (Single Labeled Surface) mm
    Bone surfaces with a single fluorescent label present. Primary data are collected in μm.

  • dLS (Double Labeled Surface) mm
    Bone surfaces with two fluorescent labels present. Primary data are collected in μm.

  • MS (Mineralizing Surface) mm
    MS = sLS/2+dLS.
    The logic here is that MS is the amount of surface of the bone that was mineralizing over the entire labeling period. The assumption is that some of the single label was active at the beginning of the period and some at the end. Labeling with once with calcein and once with alizarin red instead of calcein twice could help sort out this question. But, in general, labs just use calcein and say that half the single label was active at the beginning and half as active at the end. Hence, sLS/2 is the amount of single labeled surface that was active for the whole period.

  • Ir.L.Wi (Interlabel Width) μm
    The mean of all direct measurements of distance between labels in double labeled surfaces, corrected by a known stereology conversion constant of 1.2 which converts from measuring a straight distance in the plane to a straight distance in space. Distances are measured perpendicularly at regular intervals along the surface. Primary data are in collected μm.

  • Ir.L.t (Interlabel Time) days
    The time between injections used to label the mineralizing surfaces.

  • MAR (Mineral Apposition Rate) μm/day
    MAR = (Ir.L.Wi/1.2)/Ir.L.t.n

  • Aj.AR (Adjusted Apposition Rate) μm/day
    If MS/OS < 1, then Aj.Ar = MAR*MS/OS. If MS/OS > 1, Aj.Ar = MAR.

  • BFR/BS (Bone Formation Rate, Normalized by Bone Surface) μm/day
    BFR/BS = MAR*MS/BS.

  • BFR/BV (Bone Formation Rate, Normalized by Bone Volume) (μm/day)/mm
    BFR/BV = MAR*MS/BV.

  • BFR/TV (Bone Formation Rate, Normalized by Tissue Volume) (μm/day)/mm
    BFR/TV = MAR*MS/TV.

  • Omt (Osteoid Maturation Time) days
    O.Wi/MAR.

REMODELING INDICES

  • W.Th (Wall Thickness) mcm
    Average(W.Th)/1.2.
    The mean of all wall thickness measurements in the biopsy corrected by a known stereology constant of 1.2. Widths are measured perpendicularly at regular intervals along a surface. Primary data are collected in μm.

A Note about Dimensionality in Naming Conventions

Primary bone data collected from histology is either area (two dimensional), length (one dimensional), or number ( zero dimensional) data. Yet, final histomorphometry data are usually reported in terms of volume (three dimensional), surface (two dimensional), and number (still zero dimensional). This tradition comes from a few equations in the field of "stereology," the study of statistical methods to analyze three dimensional structures from a limited number of two dimensional sections.

For example, the Delesse Principle holds that B.Ar/T.Ar is proportional to BV/TV. (The bone area to tissue area ratio in a section is proportional to the bone volume to tissue volume ratio in the whole trabecular compartment.) Therefore, it might be more accurate to name primary data arrays in BIOQUANT using area and perimeter (B.Ar, B.Pm), and to name computed arrays using volume ans surface (BV, BS). Certainly the nomenclature committee allows for this and provides the necessary abbreviations. In practice, however, this proved counter-intuitive.

BIOQUANT decided to use the volume, surface, and number terminology for both primary data and computed data. This consistency of naming makes it easy to track data through their various computations. Combined with clear labeling of units, this seems to balance the needs of conceptual clarity and computational accuracy.

A Note on the Various Abbreviations for Microns

In BIOQUANT, primary data are collected in calibrated units, normally microns (μm) and square microns (μm2). The ASBMR nomenclature committee reports uses the abbreviation mcm to refer to microns. BIOQUANT uses the mcm convention in its unit labels to maintain consistency with the nomenclature committee.

Footnotes

a Included here because of rekindled interest in assessing adipocyte parameters in the marrow space of iliac crest bone biopsies and the shared progenitor cell with osteoblasts.

b 2D or 3D refers to the format in which data are reported, not the dimensions of an individual quantity.

c Also day, but context should eliminate ambiguity.

d endocortical + cancellous

e As a process, not as a morphologic feature.

f Between osteoid and mineralized bone.

g If unqualified, osteocytic, not Howship's

h For example, subjects, sites, sections, etc.

i An individual structure, not a type of tissue.

j The 2012 update specifically mentions that, in the context of bone biology, the term density should be, "restricted to as far as possible to its primary meaning in physics of mass per unit volume, with a subsidiary meaning analogous to population density, which is applied mainly to cells."

k As a morphologic feature, not as a process.